The present invention relates to correcting systematic errors in digital-to-analog converters (DACs). DAC designers desire to make accurate linear converters such that the output analog voltage is a linear function of the digital input code. However, DAC components often introduce errors into the DAC, which add non-linear errors to the linear transform function leading to inaccurate DACs.
The errors can be divided into two groups: Non-systematic and systematic errors. Non-systematic errors are random, unpredictable errors that are insensitive to other characteristics of the converter. Non-systematic errors are often introduced in the manufacturing process. For example, device mismatch may arise randomly among different manufacturing lots of a common integrated circuit. Since these errors are insensitive to other parts, the errors, generally, can be defined in classes.
Systematic errors, on the other hand, are predictable and are the result from specific DAC components. Systematic errors also vary according to some variable (e.g. voltage, temperature). For example, some integrated DACs include SiCr thin-film resistors (TFRs). Even though TFRs provide better linearity than polysilicon or diffusion resistors, TFRs still introduce non-linearity errors into the DAC transfer function because TFRs, generally, dissipate power and heat over themselves. The power and heat dissipation alter the resistance of TFR when the temperature coefficient of resistance is non-zero leading to the largest source of non-linearity error in a TFR. Consequently, a DAC including TFRs may show non-linear behavior due to the non-linearity of the TFR.
The non-linearity behavior depends on the DAC operating voltage. Therefore, larger operating voltages correspond to greater non-linearity errors because larger operating voltages dissipate more power and heat in its constituent TFR. With respect to an ideal linear two-terminal resistor, Ohm's Law states that the voltage and current are linearly related as:V=I*R, where V is voltage, I is the current, and R is the resistance, which is a constant. However, in real world conditions two terminal resistors are subject to self-heating effects that leads to non-linearity effects. Due to the non-linearity effects, the resistance R varies according to the power in the resistor as:R(V)=Ro{1+KV2},where Ro is the ideal linear resistance value and K is a heating coefficient that is a constant. Since K is typically a small number, the non-linear term of the equation is smaller than the linear term.
Accordingly, the relationship between the voltage and current transforms to:V=I*R(V)=I*Ro{1+KV2}As seen by the above equation, the non-linearity errors introduced by the heating effects are dependant on the voltage. Thus, heating effects on the resistors can be categorized as systematic errors. Other converter components, such as capacitors, can also lead to systematic errors.
There is a need in the art for an error correction network that creates specific counter distortion in response to the identified systematic non-linearity errors.